I'm hoping someone canhelp me with a poker math question. Recently I played a session of $25 Zone, 6max and had the following situation(s) occur. I saw the flop with suited cards 41 times and never had a single card in the suit I held hit the flop. Was hoping someone could show me how to figure the odds of that happening. Thank you.

Do you mean the odds of it ever happening? Or the odds of it happening in the next 41 times?

The odds of it ever happening.

OP, are you sure you described this properly? you say 41 times in a row, you never hit a suited card..... seems bizarre. and I have odds at (1 in 151 trillion) of that happening if we starting dealing cards right now and play until situation happens up to 41 times (we stop if you get suited card on flop)

if you play tons of poker in your lifetime... it's probably 1 in 300 billion (my guess) that it would ever happen to you in your lifetime .

here's the math. and I will simplify it.

there are 11 cards that could hit out of 50 for first flop card. then 11/49 and 11/50........... but let's simplify and say 20% chance each of the 3 cards.......

so your odds of at least 1 suited card is...

20% + 20% * (80%) + 20% * (64%) = 46.6%

odds of not hitting = 53.4% .... 46.4% ^ 41 = 2.2 * 10^-14 probability..

so I think you did not describe situation properly.

I found an error partway thorough my comments so I hope if fixed it in all places..... it's approx. 50% that you won't get one of suited cards on the flop.... so it's like losing 41 coin flips in a row.... see binomial calculator.;.... might still be slight error but very slight

note: many people think "why isn't it 20% * 3 = 60% chance of getting suited card"?... but that math includes being dealt multiple suited cards on flop... the Exp # of suited cards on flop = .6..

100%

Yes. The only reasonable way to answer this question is the chance such a sequence happens starting with the very next deal. That's how all poker deal probabilities are framed.

Thank you very much for your answer; and yes, 41 times in a row without a single suited card hitting the flop. I keep very accurate records and reviewed my hand history twice to be sure i didn't make a mistake. Strangely enough, one of several 'bizarre' happenings that I've experienced on (r)ignition poker.

Bet you can't do it again...

You approximated the probability of hitting exactly one suited card on the flop. It's easier to directly compute the probability that no suited card hits the flop. That's
P(miss the first)*P(miss second GIVEN missed first)*P(miss third GIVEN missed first two)

= (39/50)(39/49)(39/48) = 50.4%

even closer to 50% than you thought.


PairTheBoard

I run exceptionally bad on bov/ignition

Please disregard my previous response to your post. Your method is exactly right. My method was right but the numbers should have been:

(39/50)(38/49)(37/48) = 0.466

which agrees with your result. Sorry for my confusion.


PairTheBoard